Question: The sum of $5$ consecutive integers is $460$. What is the fifth number in this sequence?
Solution: Call the first number in the sequence $x$ The next integer in the sequence is $x + 1$ The sum of the $5$ consecutive integers is: $x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4) = 460$ $5x + 10= 460$ $5x = 450$ $x = 90$ Since $x$ is the first number, $x + 4$ is the fifth integer. Thus, the fifth number in the sequence is $94$.